Nonequilibrium Dynamics of Simple Exclusion Processes Across Dimensions
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Abstract (arXiv)
The simple exclusion process (SEP) is a paradigmatic model for nonequilibrium transport, yet its rich dynamics over an exponentially large configuration space remain notoriously intractable. Here, we leverage variational autoregressive networks to characterize the nonequilibrium dynamics of the symmetric (SSEP), asymmetric (ASEP), and totally asymmetric (TASEP) cases in one to three dimensions at any time. We validate the approach against established finite-time 1D and long-time 2D results for the SSEP, and further provide new results on dynamical activity, density fields and nonequilibrium phase transitions for 2D and 3D cases. In 2D, we give a directional-density criterion connecting the bulk-density organization to the 1D TASEP phase diagram, and reveal how boundary and bulk rates separately control the activity and susceptibility. In 3D, we provide the first finite-time characterization of the SSEP active-inactive phase transition, and uncover scaling relations over time. Across dimensions, the critical field follows a trend sc~ L-2, suggesting tuning strategies by the characteristic diffusive length scale. Overall, this work establishes a unified neural-network framework for characterizing nonequilibrium dynamics of representative transport systems.
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References · 10
- 2015MADE: Masked Autoencoder for Distribution Estimationcited by 307
- 2018Solving Statistical Mechanics Using Variational Autoregressive Networkscited by 100
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- 2022Neural-network solutions to stochastic reaction networkscited by 8
- 2020Dynamical large deviations of two-dimensional kinetically constrained models using a neural-network state ansatzcited by 6
- 2025WeightFlow: Learning Stochastic Dynamics via Evolving Weight of Neural Networkcited by 4
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